Literal Equations: Rearranging Formulas

What is a literal equation?

A literal equation contains multiple variables (letters). Solving for one variable means isolating it on one side — the same inverse-operation process as solving a regular equation, but the answer contains other variables instead of numbers.

Step-by-step solution: solve $A = P(1 + rt)$ for $r$

Step 1 — Divide both sides by $P$ to undo the multiplication:

$\frac{A}{P} = 1 + rt$

Step 2 — Subtract 1 from both sides to isolate the term with $r$:

$\frac{A}{P} - 1 = rt$

Step 3 — Divide both sides by $t$ to isolate $r$:

$r = \frac{A/P - 1}{t} = \frac{A - P}{Pt}$

Check: Substitute back: $P(1 + \frac{A-P}{Pt} \cdot t) = P(1 + \frac{A-P}{P}) = P \cdot \frac{A}{P} = A$ ✓

The key principle

The same inverse operations you use for $3x + 7 = 22$ apply here — just treat every other variable as if it were a number.

Common mistakes

• Forgetting to distribute. In $A = P + Prt$, students sometimes divide only part by $P$.
• Wrong order of operations. Undo addition/subtraction before multiplication/division.

Try it in the visualization

Select from several common formulas. Each step is shown on a balance scale metaphor. Plug in test values to verify.